7/6-4/3n=-3/2n+2

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Solution for 7/6-4/3n=-3/2n+2 equation:



7/6-4/3n=-3/2n+2
We move all terms to the left:
7/6-4/3n-(-3/2n+2)=0
Domain of the equation: 3n!=0
n!=0/3
n!=0
n∈R
Domain of the equation: 2n+2)!=0
n∈R
We get rid of parentheses
-4/3n+3/2n-2+7/6=0
We calculate fractions
84n^2/216n^2+(-288n)/216n^2+324n/216n^2-2=0
We multiply all the terms by the denominator
84n^2+(-288n)+324n-2*216n^2=0
We add all the numbers together, and all the variables
84n^2+324n+(-288n)-2*216n^2=0
Wy multiply elements
84n^2-432n^2+324n+(-288n)=0
We get rid of parentheses
84n^2-432n^2+324n-288n=0
We add all the numbers together, and all the variables
-348n^2+36n=0
a = -348; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-348)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-348}=\frac{-72}{-696} =3/29 $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-348}=\frac{0}{-696} =0 $

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